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    "###### Content under Creative Commons Attribution license CC-BY 4.0, code under BSD 3-Clause License © 2018 parts of this notebook are from [this Jupyter notebook](https://nbviewer.jupyter.org/github/krischer/seismo_live/blob/master/notebooks/Computational%20Seismology/The%20Finite-Difference%20Method/fd_ac1d.ipynb) by Heiner Igel ([@heinerigel](https://github.com/heinerigel)), Lion Krischer ([@krischer](https://github.com/krischer)) and Taufiqurrahman ([@git-taufiqurrahman](https://github.com/git-taufiqurrahman)) which is a supplemenatry material to the book [Computational Seismology: A Practical Introduction](http://www.computational-seismology.org/),  additional modifications by D. Koehn, notebook style sheet by L.A. Barba, N.C. Clementi"
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    "# Execute this cell to load the notebook's style sheet, then ignore it\n",
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   "cell_type": "markdown",
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   "source": [
    "# FD stability and dispersion\n",
    "\n",
    "In the [last lesson](http://nbviewer.jupyter.org/github/daniel-koehn/Theory-of-seismic-waves-II/blob/master/03_Intro_finite_differences/2_fd_ac1d.ipynb) we developed a 1D acoustic FD modelling code. For the given modelling parameters, the code worked flawlessly and delivered modelled seismograms, which are in good agreement with the analytical solution. In this lesson we want to investigate how to choose optimum time steps dt and spatial grid point distances dx, to get stable and accurate FD modelling results. We start, by revisiting a simplified version of our 1D acoustic FD modelling code ..."
   ]
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  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "code_folding": [
     0
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   "source": [
    "# Import Libraries \n",
    "# ----------------\n",
    "import numpy as np\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "from pylab import rcParams\n",
    "\n",
    "# Ignore Warning Messages\n",
    "# -----------------------\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "code_folding": [],
    "scrolled": false
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   "source": [
    "# Definition of modelling parameters\n",
    "# ----------------------------------\n",
    "xmax = 500 # maximum spatial extension of the 1D model (m)\n",
    "dx   = 0.5 # grid point distance in x-direction\n",
    "\n",
    "tmax = 1.001   # maximum recording time of the seismogram (s)\n",
    "dt   = 0.0010  # time step\n",
    "\n",
    "vp0  = 333.   # P-wave speed in medium (m/s)\n",
    "\n",
    "# acquisition geometry\n",
    "xr = 365.0 # receiver position (m)\n",
    "xsrc = 249.5 # source position (m)\n",
    "\n",
    "f0   = 25. # dominant frequency of the source (Hz)\n",
    "t0   = 4. / f0 # source time shift (s)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Comparison of numerical with analytical solution\n",
    "\n",
    "In the function below we solve the homogeneous 1D acoustic wave equation by the 3-point spatial/temporal difference operator and compare the numerical results with the analytical solution. To play a little bit more with the modelling parameters, I restricted the input parameters to dt and dx. The number of spatial grid points and time steps, as well as the discrete source and receiver positions are estimated within this function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "code_folding": [
     42
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   "source": [
    "# 1D Wave Propagation (Finite Difference Solution) \n",
    "# ------------------------------------------------\n",
    "def FD_1D_acoustic(dt,dx,spec):\n",
    "        \n",
    "    nx = (int)(xmax/dx) # number of grid points in x-direction\n",
    "    print('nx = ',nx)\n",
    "        \n",
    "    nt = (int)(tmax/dt) # maximum number of time steps            \n",
    "    print('nt = ',nt)\n",
    "    \n",
    "    ir = (int)(xr/dx)      # receiver location in grid in x-direction    \n",
    "    isrc = (int)(xsrc/dx)  # source location in grid in x-direction\n",
    "\n",
    "    # Source time function (Gaussian)\n",
    "    # -------------------------------\n",
    "    src  = np.zeros(nt + 1)\n",
    "    time = np.linspace(0 * dt, nt * dt, nt)\n",
    "\n",
    "    # 1st derivative of a Gaussian\n",
    "    #src  = -2. * (time - t0) * (f0 ** 2) * (np.exp(- (f0 ** 2) * (time - t0) ** 2))\n",
    "    \n",
    "    # 2nd derivative of a Gaussian\n",
    "    src = (1.0 - 2.0*(np.pi**2)*(f0**2)*((time-t0)**2)) * np.exp(-(np.pi**2)*(f0**2)*((time-t0)**2))\n",
    "\n",
    "    # Analytical solution\n",
    "    # -------------------\n",
    "    G    = time * 0.\n",
    "\n",
    "    # Initialize coordinates\n",
    "    # ----------------------\n",
    "    x    = np.arange(nx)\n",
    "    x    = x * dx       # coordinate in x-direction\n",
    "\n",
    "    for it in range(nt): # Calculate Green's function (Heaviside function)\n",
    "        if (time[it] - np.abs(x[ir] - x[isrc]) / vp0) >= 0:\n",
    "            G[it] = 1. / (2 * vp0)\n",
    "    Gc   = np.convolve(G, src * dt)\n",
    "    Gc   = Gc[0:nt]\n",
    "    lim  = Gc.max() # get limit value from the maximum amplitude\n",
    "    \n",
    "    # Initialize empty pressure arrays\n",
    "    # --------------------------------\n",
    "    p    = np.zeros(nx) # p at time n (now)\n",
    "    pold = np.zeros(nx) # p at time n-1 (past)\n",
    "    pnew = np.zeros(nx) # p at time n+1 (present)\n",
    "    d2px = np.zeros(nx) # 2nd space derivative of p\n",
    "\n",
    "    # Initialize model (assume homogeneous model)\n",
    "    # -------------------------------------------\n",
    "    vp    = np.zeros(nx)\n",
    "    vp    = vp + vp0       # initialize wave velocity in model\n",
    "\n",
    "    # Initialize empty seismogram\n",
    "    # ---------------------------\n",
    "    seis = np.zeros(nt) \n",
    "    \n",
    "    # Calculate Partial Derivatives\n",
    "    # -----------------------------\n",
    "    for it in range(nt):\n",
    "    \n",
    "        # FD approximation of spatial derivative by 3 point operator\n",
    "        for i in range(1, nx - 1):\n",
    "            d2px[i] = (p[i + 1] - 2 * p[i] + p[i - 1]) / dx ** 2\n",
    "\n",
    "        # Time Extrapolation\n",
    "        # ------------------\n",
    "        pnew = 2 * p - pold + vp ** 2 * dt ** 2 * d2px\n",
    "\n",
    "        # Add Source Term at isrc\n",
    "        # -----------------------\n",
    "        # Absolute pressure w.r.t analytical solution\n",
    "        pnew[isrc] = pnew[isrc] + src[it] / dx * dt ** 2\n",
    "                \n",
    "        # Remap Time Levels\n",
    "        # -----------------\n",
    "        pold, p = p, pnew\n",
    "    \n",
    "        # Output of Seismogram\n",
    "        # -----------------\n",
    "        seis[it] = p[ir]   \n",
    "        \n",
    "    # Compare FD Seismogram with analytical solution\n",
    "    # ---------------------------------------------- \n",
    "    # Define figure size\n",
    "    fig1 = plt.figure(figsize=(12, 5))\n",
    "    plt.plot(time, seis, 'b-',lw=3,label=\"FD solution\") # plot FD seismogram\n",
    "    Analy_seis = plt.plot(time,Gc,'r--',lw=3,label=\"Analytical solution\") # plot analytical solution\n",
    "    plt.xlim(time[0], time[-1])\n",
    "    plt.ylim(-lim, lim)\n",
    "    plt.title('Seismogram')\n",
    "    plt.xlabel('Time (s)')\n",
    "    plt.ylabel('Amplitude')\n",
    "    plt.legend()\n",
    "    plt.grid()\n",
    "    \n",
    "    # Plot amplitude spectrum of seismogram\n",
    "    if(spec==True):\n",
    "        fig2 = plt.figure(figsize=(12, 5))\n",
    "        spec = np.fft.fft(src) # source time function in frequency domain\n",
    "        freq = np.fft.fftfreq(spec.size, d = dt) # time domain to frequency domain\n",
    "        plt.plot(np.abs(freq), np.abs(spec)) # plot frequency and amplitude\n",
    "        plt.xlim(0, 70) # only display frequency from 0 to 250 Hz\n",
    "        plt.title('Amplitude Spectrum (Source Wavelet)')\n",
    "        plt.xlabel('Frequency (Hz)')\n",
    "        plt.ylabel('|FFT(src)|')\n",
    "        \n",
    "    plt.show()            "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "nx =  1000\n",
      "nt =  1000\n"
     ]
    },
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\n",
      "text/plain": [
       "<Figure size 864x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "dx   = 0.5 # grid point distance in x-direction\n",
    "dt   = 0.0010  # time step\n",
    "FD_1D_acoustic(dt,dx,True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is the same result, we achieved in the last lesson. Now, you might get the smart idea to save some computation time by increasing the timestep dt. Let's try it ... "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "nx =  1000\n",
      "nt =  664\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "dx   = 0.5 # grid point distance in x-direction\n",
    "#dt   = 0.0010  # old time step\n",
    "dt   = 0.0015053  # time step\n",
    "FD_1D_acoustic(dt,dx,False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Oops, maybe this idea was not so smart at all, because the modelling becomes **unstable**. Instead of increasing the time step dt, we could try to increase the spatial discretization dx to save computation time ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "nx =  250\n",
      "nt =  1000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# dx   = 0.5 # old grid point distance in x-direction\n",
    "dx   = 2.0 # new grid point distance in x-direction\n",
    "dt   = 0.0010  # time step\n",
    "FD_1D_acoustic(dt,dx,False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hmm, the accurracy of the FD modelling result compared to the analytical solution is clearly deterioated, when the spatial grid point $dx$ is increased. And why does the P-body wave becomes dispersive? More generally, how do I choose $dx$ and $dt$ without using a trial-and-error approach, which requires a lot of computation time, especially when considering 3D modelling. To understand the underlying problems, we will investigate the stability and numerical dispersion of the FD method in the next two sections."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Stability of 1D acoustic wave equation finite difference approximation\n",
    "\n",
    "To analyse the stability of the finite difference approximation of the 1D acoustic wave equation:\n",
    "\n",
    "\\begin{equation}\n",
    " \\frac{p_{j}^{n+1} - 2 p_{j}^n + p_{j}^{n-1}}{\\mathrm{d}t^2} \\ = \\ vp_{j}^2 \\frac{p_{j+1}^{n} - 2 p_{j}^n + p_{j-1}^{n}}{\\mathrm{d}x^2},\n",
    "\\end{equation}\n",
    "\n",
    "we use an approach introduced by the famous mathematician and pioneer of computational sciences [John von Neumann](https://en.wikipedia.org/wiki/John_von_Neumann). For the **von Neumann Analysis**, we assume harmonic plane wave solutions for the pressure wavefield like:\n",
    "\n",
    "\\begin{equation}\n",
    "p = exp(i(kx-\\omega t)),\\nonumber\n",
    "\\end{equation}\n",
    "\n",
    "with $i^2=-1$, the wavenumber $k$ and circular frequency $\\omega$. Using the discrete \n",
    "spatial coordinates:\n",
    "\n",
    "$x_j = j dx,$\n",
    "\n",
    "and times \n",
    "\n",
    "$t_n = n dt.$\n",
    "\n",
    "We can calculate discrete plane wave solutions at the discrete locations and times in eq. (1), for example at grid point j and time n:  \n",
    "\n",
    "\\begin{equation}\n",
    "p_j^n = exp(i(kjdx-\\omega n dt)),\\nonumber\n",
    "\\end{equation}\n",
    "\n",
    "or at grid point j and time n+1:\n",
    "\n",
    "\\begin{align}\n",
    "p_j^{n+1} &= exp(i(kjdx-\\omega (n+1) dt))\\nonumber\\\\\n",
    "&= exp(-i\\omega dt)\\; exp(i(kjdx-\\omega n dt))\\nonumber\\\\\n",
    "&= exp(-i\\omega dt)\\; p_j^n,\\nonumber\\\\\n",
    "\\end{align}\n",
    "\n",
    "or at the grid point j and time n-1:\n",
    "\n",
    "\\begin{align}\n",
    "p_j^{n-1} &= exp(i(kjdx-\\omega (n-1) dt))\\nonumber\\\\\n",
    "&= exp(i\\omega dt)\\; exp(i(kjdx-\\omega n dt))\\nonumber\\\\\n",
    "&= exp(i\\omega dt)\\; p_j^n.\\nonumber\\\\\n",
    "\\end{align}\n",
    "\n",
    "Similar approximations can be estimated for time n at the spatial grid points j+1:\n",
    "\n",
    "\\begin{align}\n",
    "p_{j+1}^{n} &= exp(i(k(j+1)dx-\\omega n dt))\\nonumber\\\\\n",
    "&= exp(ik dx)\\; exp(i(kjdx-\\omega n dt))\\nonumber\\\\\n",
    "&= exp(ik dx)\\; p_j^n,\\nonumber\\\\\n",
    "\\end{align}\n",
    "\n",
    "and a grid point j-1:\n",
    "\n",
    "\\begin{align}\n",
    "p_{j-1}^{n} &= exp(i(k(j-1)dx-\\omega n dt))\\nonumber\\\\\n",
    "&= exp(-ik dx)\\; exp(i(kjdx-\\omega n dt))\\nonumber\\\\\n",
    "&= exp(-ik dx)\\; p_j^n.\\nonumber\\\\\n",
    "\\end{align}\n",
    "\n",
    "Inserting the discrete pressure wavefield solutions $p_j^{n+1}$, $p_j^{n-1}$, $p_{j+1}^{n}$ and $p_{j-1}^{n}$ in eq. (1), we get after some minor rearrangement:\n",
    "\n",
    "\\begin{equation}\n",
    "exp(-i\\omega dt)p_j^n - 2 p_j^n + exp(i\\omega dt)p_j^n = vp_j^2 \\frac{dt^2}{dx^2}\\biggl(exp(-ik dx)p_j^n - 2 p_j^n + exp(ik dx)p_j^n\\biggr).\\nonumber\n",
    "\\end{equation}\n",
    "\n",
    "Assuming that $p_j^n \\ne 0$, we can divide the RHS and LHS by $p_j^n$\n",
    "\n",
    "\\begin{equation}\n",
    "exp(-i\\omega dt) - 2 + exp(i\\omega dt) = vp_j^2 \\frac{dt^2}{dx^2}\\biggl(exp(-ik dx) - 2 + exp(ik dx)\\biggr).\\nonumber\n",
    "\\end{equation}\n",
    "\n",
    "By further dividing RHS and LHS by 2, we get:\n",
    "\n",
    "\\begin{equation}\n",
    "\\frac{exp(i\\omega dt) + exp(-i\\omega dt)}{2} - 1 = vp_j^2 \\frac{dt^2}{dx^2}\\biggl(\\frac{exp(ik dx) + exp(-ik dx)}{2} - 1\\biggr).\\nonumber\n",
    "\\end{equation}\n",
    "\n",
    "Using the definition \n",
    "\n",
    "\\begin{equation}\n",
    "\\cos(x) = \\frac{exp(ix) + exp(-ix)}{2},\\nonumber\n",
    "\\end{equation}\n",
    "\n",
    "we can simplify this expression to:\n",
    "\n",
    "\\begin{equation}\n",
    "cos(\\omega dt) - 1 = vp_j^2 \\frac{dt^2}{dx^2}\\biggl(cos(k dx) - 1\\biggr).\\nonumber\n",
    "\\end{equation}\n",
    "\n",
    "After some further rearrangements and division of both sides by 2, leads to:\n",
    "\n",
    "\\begin{equation}\n",
    "\\frac{1 - cos(\\omega dt)}{2} = vp_j^2 \\frac{dt^2}{dx^2}\\biggl(\\frac{1 - cos(k dx)}{2}\\biggr).\\nonumber\n",
    "\\end{equation}\n",
    "\n",
    "With the relation \n",
    "\n",
    "\\begin{equation}\n",
    "sin^2\\biggl(\\frac{x}{2}\\biggr) = \\frac{1-cos(x)}{2}, \\nonumber\n",
    "\\end{equation}\n",
    "\n",
    "we get \n",
    "\n",
    "\\begin{equation}\n",
    "sin^2\\biggl(\\frac{\\omega dt}{2}\\biggr) = vp_j^2 \\frac{dt^2}{dx^2}\\biggl(sin^2\\biggl(\\frac{k dx}{2}\\biggr)\\biggr).\\nonumber\n",
    "\\end{equation}\n",
    "\n",
    "Taking the square root of both sides finally leads to \n",
    "\n",
    "\\begin{equation}\n",
    "sin\\frac{\\omega dt}{2} = vp_j \\frac{dt}{dx}\\biggl(sin\\frac{k dx}{2}\\biggr).\n",
    "\\end{equation}\n",
    "\n",
    "This result is quite interesting. Notice, that the amplitude of the sine functions $sin(x)$ on the LHS and RHS vary between -1 and 1. However, if the factor on the RHS\n",
    "\n",
    "\\begin{equation}\n",
    "\\epsilon = vp_j \\frac{dt}{dx} \\nonumber\n",
    "\\end{equation}\n",
    "\n",
    "is larger 1 ($\\epsilon>1$), you get only complex solutions. \n",
    "\n",
    "Consequently, the numerical scheme becomes unstable. Therefore, the criterion\n",
    "\n",
    "\\begin{equation}\n",
    "\\epsilon = vp_j \\frac{dt}{dx} \\le 1 \\nonumber\n",
    "\\end{equation}\n",
    "\n",
    "has to be satisfied. This very important stability criterion was first described by the german-american mathematicians Richard Courant, Kurt Friedrichs and Hans Lewy in [this paper](https://gdz.sub.uni-goettingen.de/id/PPN235181684_0100?tify={%22pages%22:[36],%22view%22:%22thumbnails%22}) from 1928. The **Courant-Friedrichs-Lewy criterion** or in short **CFL-criterion**, can also be rearranged to the time step dt, assuming that we have defined a spatial grid point distance dx:\n",
    "\n",
    "\\begin{equation}\n",
    "dt  \\le \\frac{dx}{vp_j}. \\nonumber\n",
    "\\end{equation}\n",
    "\n",
    "This criterion is only correct for the FD solution of the 1D acoustic wave equation using the 3-point spatial/temporal FD operators and an explicit time-stepping scheme (eq.(1)).\n",
    "\n",
    "More generally, we can write the Courant criterion as \n",
    "\n",
    "\\begin{equation}\n",
    "dt  \\le \\frac{dx}{\\zeta vp_j}, \\nonumber\n",
    "\\end{equation}\n",
    "\n",
    "where the factor $\\zeta$ depends on the used FD operator, dimension of the problem (1D, 2D, 3D) and the overall algorithm. Even though the CFL criterion strictly depends on the P-wave velocity at a specific grid point, in most cases the maximum velocity $v_{max}$ in the medium is used to estimate a constant time step $dt$ for the whole FD modelling run:\n",
    "\n",
    "\\begin{equation}\n",
    "dt  \\le \\frac{dx}{\\zeta v_{max}}, \\nonumber\n",
    "\\end{equation}\n",
    "\n",
    "where $v_{max}$ is the maximum P-wave velocity in the acoustic case or the maximum S-wave velocity for the SH-problem. While the fulfillment of the CFL criterion leads to a stable simulation, it does not guarantee accurate modelling results. \n",
    "\n",
    "The CFL criterion allows us to estimate an appropriate time step dt based on the maximum velocity in the model and the spatial grid point distance. But how do we choose the spatial gridpoint distance dx?\n",
    "\n",
    "##### Exercise\n",
    "\n",
    "Let 's investigate the statement, that equation (2) delivers only complex solutions if $\\epsilon>1$. Try to find solutions to the following simple problem \n",
    "\n",
    "\\begin{equation}\n",
    "\\sin(x) = 2 \\nonumber\n",
    "\\end{equation}\n",
    "\n",
    "**Hint**\n",
    "\n",
    "Use Eulers identity $e^{iy} = cos(y) + i sin(y)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Numerical grid dispersion\n",
    "\n",
    "In the modelling examples at the beginning of this Jupyter notebook, we have seen that the modelled wavefield can become subject to dispersion, when choosing a too large spatial grid point distance. The result of the von Neumann analysis can also explain this behaviour. Starting from eq. (2)\n",
    "\n",
    "\\begin{equation}\n",
    "sin\\frac{\\omega dt}{2} = \\epsilon\\; sin\\frac{k dx}{2}, \\nonumber\n",
    "\\end{equation}\n",
    "\n",
    "we apply the $arcsin$ to both sides\n",
    "\n",
    "\\begin{equation}\n",
    "\\frac{\\omega dt}{2} = arcsin\\biggl(\\epsilon\\; sin\\frac{k dx}{2} \\biggr)\\nonumber\n",
    "\\end{equation}\n",
    "\n",
    "and multiply the result by $\\frac{2}{dt}$, we get\n",
    "\n",
    "\\begin{equation}\n",
    "\\omega = \\frac{2}{dt}arcsin\\biggl(\\epsilon\\; sin\\frac{k dx}{2}\\biggr)\\nonumber\n",
    "\\end{equation}\n",
    "\n",
    "Inserting this $\\omega-k$ dependence into the definition of the phase velocity \n",
    "\n",
    "\\begin{equation}\n",
    "v_{phase} = \\frac{\\omega}{k},\\nonumber\n",
    "\\end{equation}\n",
    "\n",
    "leads to \n",
    "\n",
    "\\begin{equation}\n",
    "v_{phase} = \\frac{2}{k dt}arcsin\\biggl(\\epsilon\\; sin\\frac{k dx}{2}\\biggr).\\nonumber\n",
    "\\end{equation}\n",
    "\n",
    "As you can see, the phase velocity of the numerical FD solution is a function of the wavenumber k. Therefore, it can be subject to dispersion. To investigate this problem in more detail, we rewrite the phase velocity.\n",
    "\n",
    "With the wavenumber $k=\\frac{2 \\pi}{\\lambda}$, where $\\lambda$ denotes the wavelength, we get:\n",
    "\n",
    "\\begin{equation}\n",
    "v_{phase} = \\frac{\\lambda}{\\pi dt}arcsin\\biggl(\\epsilon\\; sin\\frac{\\pi dx}{\\lambda}\\biggr).\\nonumber\n",
    "\\end{equation}\n",
    "\n",
    "From the definition of $\\epsilon = vp_0 \\frac{dt}{dx}$, we can replace $dt$ by $dt = \\frac{\\epsilon dx}{vp_0}$ in the phase velocity:\n",
    "\n",
    "\\begin{equation}\n",
    "v_{phase} = \\frac{\\lambda vp_0}{\\pi \\epsilon dx}arcsin\\biggl(\\epsilon\\; sin\\frac{\\pi dx}{\\lambda}\\biggr).\\nonumber\n",
    "\\end{equation}\n",
    "\n",
    "Introducing the **number of grid points per wavelength** $N_\\lambda = \\frac{\\lambda}{dx}$, we finally get:\n",
    "\n",
    "\\begin{equation}\n",
    "v_{phase} = \\frac{N_\\lambda vp_0}{\\pi \\epsilon}arcsin\\biggl(\\epsilon\\; sin\\frac{\\pi }{N_\\lambda}\\biggr).\\nonumber\n",
    "\\end{equation}\n",
    "\n",
    "Let's plot this result for $N_\\lambda$ between 2 and 12, the homogeneous P-wave velocity $vp0\\;=\\;333\\;m/s$, and $\\epsilon$ values form 0.7 to 1.0 ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "Nwave = np.arange(2,12,0.25) # numbers per wavelength\n",
    "vp0 = 333.0 # P-wave velocity (m/s)\n",
    "\n",
    "def dispersion_1D(eps):\n",
    "    \n",
    "    vp_phase = (vp0*Nwave/(np.pi*eps)) * np.arcsin(eps*np.sin(np.pi/Nwave)) \n",
    "    \n",
    "    return vp_phase"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "vp_eps_1 = dispersion_1D(1.0)\n",
    "vp_eps_2 = dispersion_1D(0.9)\n",
    "vp_eps_3 = dispersion_1D(0.8)\n",
    "vp_eps_4 = dispersion_1D(0.7)\n",
    "\n",
    "rcParams['figure.figsize'] = 12, 5\n",
    "plt.plot(Nwave, vp_eps_1, 'b-',lw=3,label=r\"$\\epsilon=1$\")\n",
    "plt.plot(Nwave, vp_eps_2, 'r-',lw=3,label=r\"$\\epsilon=0.9$\") \n",
    "plt.plot(Nwave, vp_eps_3, 'g-',lw=3,label=r\"$\\epsilon=0.8$\") \n",
    "plt.plot(Nwave, vp_eps_4, 'k-',lw=3,label=r\"$\\epsilon=0.7$\") \n",
    "plt.title('Grid dispersion')\n",
    "plt.xlabel('Number of grid points per wavelength')\n",
    "plt.ylabel('Phase velocity $v_{phase}$, m/s')\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.show() "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice, that no grid dispersion occurs in the case of $\\epsilon=1$. Keep in mind though that this only true for the homogeneous medium. Realistic modelling problems have a variable P-wave velocity, so we have not a constant $\\epsilon$ within the model.\n",
    "\n",
    "For all values $\\epsilon<1$, numerical dispersion can occur, if the sampling of the spatial model is too small, especially when using only the Nyquist criterion $N_\\lambda = 2$. For the 1D acoustic wave equation, the dispersion is minimized for $N_\\lambda$ values between 8-12.\n",
    "\n",
    "More generally, we can define the **grid dispersion criterion** for the spatial gridpoint distance\n",
    "\n",
    "\\begin{equation}\n",
    "dx \\le \\frac{\\lambda_{min}}{N_\\lambda} = \\frac{v_{min}}{N_\\lambda f_{max}},\\nonumber\n",
    "\\end{equation}\n",
    "\n",
    "where $N_\\lambda$ depends on the used FD operator, numerical scheme and also wave type, $v_{min}$ is the minimum P- or S-wave velocity in the model and $f_{max}$ the maximum frequency of the source wavelet. \n",
    "\n",
    "Finally, let's apply the dispersion and stability criteria to our test problem in order to find optimum dt and dx values ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dx =  0.444\n",
      "epsilon =  1.0\n",
      "dt =  0.0013333333333333333\n",
      "nx =  1126\n",
      "nt =  750\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# calculate dx according to the grid dispersion criterion\n",
    "Nlam = 15              # number of grid points per wavelength\n",
    "fmax = 50.0            # maximum frequency of source wavelet ~ 2 * f0 (Hz)\n",
    "dx = vp0 / (Nlam*fmax) # spatial gridpoint distance (m)\n",
    "print('dx = ', dx)\n",
    "\n",
    "# calculate dt according to the CFL criterion\n",
    "dt = dx / vp0 # time step (s)\n",
    "\n",
    "# check CFL criterion\n",
    "epsilon = vp0 * dt / dx\n",
    "print('epsilon = ', epsilon)\n",
    "if(epsilon>1.0):\n",
    "    print('Warning: CFL condition is violated!')\n",
    "print('dt = ', dt)\n",
    "\n",
    "FD_1D_acoustic(dt,dx,True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## What we learned:\n",
    "\n",
    "* Estimation of the Courant-Friedrichs-Lewy (CFL) stability criterion $dt  \\le \\frac{dx}{v_{max}}$ for the 1D acoustic wave equation using the von Neumann analysis\n",
    "* Dispersion analysis of the 1D acoustic wave equation\n",
    "* Grid dispersion criterion: $dx \\le \\frac{v_{min}}{N_\\lambda f_{max}}$\n",
    "* Optimize FD modelling parameters by using the grid dispersion and CFL conditions"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
